What is x/(a^2-ax)+(a+x)/(ax)+a/(ax-x^2) ?

The solution to x/(a^2-ax)+(a+x)/(ax)+a/(ax-x^2) is (2a)/(x(-x+a))

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simplify x/(a^2-ax)+(a+x)/(ax)+a/(ax-x^2)

simplify

\frac{x}{a ^{2} - a x} + \frac{a + x}{a x} + \frac{a}{a x - x ^{2}}

\frac{2 a}{x ( - x + a )}

Solution steps

\frac{x}{a ^{2} - a x} + \frac{a + x}{a x} + \frac{a}{a x - x ^{2}}

Least Common Multiplier of

a^{2} - a x, a x, a x - x^{2} : a x (- x + a)

Adjust Fractions based on the LCM

= \frac{x ^{2}}{a x ( - x + a )} + \frac{( a + x ) ( - x + a )}{a x ( - x + a )} + \frac{a ^{2}}{a x ( - x + a )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{x ^{2} + ( a + x ) ( - x + a ) + a ^{2}}{a x ( - x + a )}

Simplify

x^{2} + (a + x) (- x + a) + a^{2} : 2 a^{2}

= \frac{2 a ^{2}}{a x ( - x + a )}

Cancel

\frac{2 a ^{2}}{a x ( - x + a )} : \frac{2 a}{x ( - x + a )}

= \frac{2 a}{x ( - x + a )}

lo g_{10} (\frac{x y ^{7}}{z ^{3}})

(x + 4) (x + 4)

\frac{100}{16}

\frac{8}{2}

(s - 1) (s - 2)

What is x/(a^2-ax)+(a+x)/(ax)+a/(ax-x^2) ?
The solution to x/(a^2-ax)+(a+x)/(ax)+a/(ax-x^2) is (2a)/(x(-x+a))